Abstract : A design theory for two flow arrangements of three-fluid heat exchangers has been developed. The dependent performance of the heat exchanger has been expressed in terms of two dimensionless quantities, termed temperature effectivenesses. The temperature effectivenesses are expressed as functions of five independent dimensionless exchanger variables, three representing operating conditions and two design conditions. This situation contrasts with one dependent and two independent dimensionless parameters for the two-fluid exchanger, a very much less complex problem. Graphs are presented showing functions of the five exchanger variables. The practical application of the design theory is shown in three examples. Insight into the problems arising in designing three-fluid heat exchangers can be achieved by inspection of the temperature effectiveness curves. (Author)